Answer:
c = velocity of light in vacuum =
\[~\left[
{{\text{M}}^{0}}{{\text{L}}^{\text{1}}}{{\text{T}}^{-\text{1}}} \right]\]
\[{{\mu
}_{0}}\]
= absolute magnetic permeability of free space =
\[~\left[
\text{ML}{{\text{T}}^{-\text{2}}}{{\text{A}}^{-\text{2}}} \right]\]
\[{{\in
}_{0}}\]
= absolute electrical permittivity of free space =
\[\left[
{{\text{M}}^{-\text{1}}}{{\text{L}}^{-\text{3}}}{{\text{T}}^{\text{4}}}{{\text{A}}^{\text{2}}}
\right]\]
.
Now, L.H.S. =
\[\text{c}=\text{ }\left[
{{\text{M}}^{0}}{{\text{L}}^{\text{1}}}{{\text{T}}^{-\text{1}}} \right]\]
R.H.S. =
\[\frac{1}{\sqrt{{{\mu }_{0}}{{\in
}_{0}}}}=\frac{1}{\sqrt{[ML{{T}^{-2}}{{A}^{-2}}][{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]}}=\frac{1}{\sqrt{{{M}^{0}}{{L}^{-2}}{{T}^{2}}}}=\text{
}\left[ {{\text{M}}^{0}}{{\text{L}}^{\text{1}}}{{\text{T}}^{-\text{1}}}
\right]\]
As L.H.S. = R.H.S., dimensionally.
\[\therefore\]
formula is correct.
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